The gender discrimination case brought against legendary Silicon Valley venture capital firm Kleiner Perkins Caufield & Byers by one of its female partners, Ellen Pao, will continue to play out in the public arena — at least for the next week, and likely for much longer.

Judge Harold Kahn ruled in San Francisco Superior Court today that Kleiner Perkins’ motion to force the case out of the court and into a more private arbitration process will be revisited on July 20, after supplemental papers have been filed. The arbitration matter was meant to be ruled on today, but two issues brought up by Kleiner — “equitable estoppel” and “3rd party beneficiary” — have pushed the decision back.

Kleiner Perkins has vigorously denied “each and every material allegation” that Pao made in the lawsuit she filed earlier this spring, but the issue at hand now is whether it should be hashing this out in court at all. Kleiner is maintaining that when joining the firm, Ellen Pao signed contractual agreements to settle legal matters through arbitration rather than through the much more public court process. The fact that she filed suit against Kleiner Perkins puts her in breach of that contract, Kleiner has said in its legal response to Pao’s claims, saying she has “sued in the incorrect forum.”

But while a final decision has not been reached yet, yesterday Judge Kahn came to a temporary ruling that Pao would not be compelled to take the case to arbitration by the employment contracts she signed — and as of now he does not seem to have changed his mind significantly. In court today, Judge Kahn said to Kleiner’s lawyer Lynne Hermle that when it comes to Pao’s contractual agreement and how it pertains to arbitration, “You and I see this case differently.” You could argue that does not seem to bode well for Kleiner’s aims to settle the matter in a more private way.

Nevertheless, now there is a bit more time for Kleiner to turn Kahn’s opinion around. Kleiner expressed optimism in a statement issued shortly after the court appointment today wrapped:

“KPCB is encouraged by Judge Kahn’s willingness to hear our arguments on third party beneficiary and equitable estoppel claims. The firm will file its motions by July 13th to be heard in a supplementary hearing on July 20th. KPCB continues to believe it has strong arguments and precedent to move the matter to arbitration. Ms. Pao, like other partners, signed a variety of standard agreements requiring, among other things, that all disputes be resolved through arbitration. We expect arbitration to be a more efficient and speedier dispute resolution process than trying a matter before a jury years down the line in the San Francisco Superior Court.”